{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Voronoi Diagrams\n",
"\n",
"Voronoi diagrams are constructed from their sites (given in homogeneous coordinates).\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1 -1/2 0\n",
"1 1/2 0\n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"$VD = new VoronoiPolyhedron(SITES=>[[1,1,1],[1,0,1],[1,-1,1],[1,1,-1],[1,0,-1],[1,-1,-1]]);\n",
"print $VD->VORONOI_VERTICES;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Actually, via lifting to the standard paraboloid, Voronoi diagrams are derived from `Polytope`. That's why they have `VERTICES`, `FACETS`, and such.\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2 -2 -2 1\n",
"1 0 -2 1\n",
"2 2 -2 1\n",
"2 -2 2 1\n",
"1 0 2 1\n",
"2 2 2 1\n",
"1 0 0 0\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print $VD->FACETS;"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 1 0 2\n",
"0 -1 0 2\n",
"0 0 1 2\n",
"0 0 -1 2\n",
"1 -1/2 0 -1\n",
"1 1/2 0 -1\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"
\n",
"Click here for additional output
\n",
"polymake: used package lrs\n",
" Implementation of the reverse search algorithm of Avis and Fukuda.\n",
" Copyright by David Avis.\n",
" http://cgm.cs.mcgill.ca/~avis/C/lrs.html\n",
"\n",
"
\n",
"
Click here for additional output
\n", "polymake: used package cdd\n", " cddlib\n", " Implementation of the double description method of Motzkin et al.\n", " Copyright by Komei Fukuda.\n", " http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/\n", "\n", "polymake: used package threejs\n", " Three.js is a lightweight cross-browser JavaScript library/API used to create and display animated 3D computer graphics on a Web browser.\n", " See http://github.com/mrdoob for the source code.\n", "\n", "\n", "